What is the bulk modulus of a material if a pressure increase of 50 MPa results
Practice Questions
Q1
What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.002 m³ for a volume of 1 m³? (2022)
25 GPa
50 GPa
100 GPa
200 GPa
Questions & Step-by-Step Solutions
What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.002 m³ for a volume of 1 m³? (2022)
Step 1: Understand the formula for bulk modulus (K), which is K = -ΔP / (ΔV/V). Here, ΔP is the change in pressure, ΔV is the change in volume, and V is the original volume.
Step 2: Identify the values given in the question. We have ΔP = 50 MPa (pressure increase) and ΔV = -0.002 m³ (volume decrease). The original volume V = 1 m³.
Step 3: Calculate the ratio ΔV/V. This is done by dividing the change in volume by the original volume: ΔV/V = -0.002 m³ / 1 m³ = -0.002.
Step 4: Substitute the values into the bulk modulus formula: K = -ΔP / (ΔV/V) = -50 MPa / (-0.002).
Step 5: Perform the calculation: K = 50 MPa / 0.002 = 25000 MPa.
Step 6: Convert the result from MPa to GPa. Since 1 GPa = 1000 MPa, we divide by 1000: 25000 MPa = 25 GPa.
